The defendant, who had pleaded "not guilty," has said he opened fire because he feared the base was coming under attack.
As he was led out of the courtroom, 1st Sgt. Marik al- Tuwayha said: "I have all the respect for the king, but I was doing my job."
The parents of one of the slain U.S. Soldiers and the father and sister of another sat quietly as the judge announced his ruling to a crowded court.
In the letter given to The Associated Press, Moriarty listed several demands to Jordan, including allowing the defendant to be re-interviewed by the FBI about his motive and releasing security camera footage of the shooting that he said was entered into the trial records.
Some of the relatives have criticized Jordan's handling of the case and called for the death penalty, saying the maximum possible sentence in this case, of life in prison, was inadequate.
The trial "confirmed that the deceased U.S. Service members followed all established procedures when accessing the base the day of the incident, as we have noted before," the U.S. Embassy in Jordan said in a statement. "We are reassured to see the perpetrator brought to justice."
The victims were 27-year-old Staff Sgt. Matthew C Lewellen of Kirksville, Missouri; 30-year-old Staff Sgt Kevin J McEnroe of Tucson, Arizona; and 27-year-old Staff Sgt. James F Moriarty of Kerrville, Texas.
The military court judge, Col. Mohammed al-Afeef, said at the start of the trial that the defendant had no known ties to militant groups.
This left questions about a possible motive.
The defendant and some of the gate guards testified that they heard what might have been a pistol shot coming from the direction of the U.S. Convoy. The defendant said he opened fire because he feared the base was coming under attack. Other guards said they held their fire because they couldn't determine the source of the sound.
However, security camera footage, as described by the bereaved relatives, shows the shooting lasted for six minutes. They have said the video shows the defendant reloading and shooting at Americans who were waving their hands and yelling: "We're Americans! We're friendly."
The video was shown to the family by US law enforcement, but has not been released to the public.
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